Revealing Dynamics, Communities, and Criticality from Data

Abstract

Complex systems such as ecological communities and neuron networks are essential parts of our everyday lives. These systems are composed of units which interact through intricate networks. The ability to predict sudden changes in the dynamics of these networks, known as critical transitions, from data is important to avert disastrous consequences of major disruptions. Predicting such changes is a major challenge as it requires forecasting the behavior for parameter ranges for which no data on the system are available. We address this issue for networks with weak individual interactions and chaotic local dynamics. We do this by building a model network, termed an effective network, consisting of the underlying local dynamics and a statistical description of their interactions. We show that behavior of such networks can be decomposed in terms of an emergent deterministic component and a fluctuation term. Traditionally, such fluctuations are filtered out. However, as we show, they are key to accessing the interaction structure. We illustrate this approach on synthetic time series of realistic neuronal interaction networks of the cat cerebral cortex and on experimental multivariate data of optoelectronic oscillators. We reconstruct the community structure by analyzing the stochastic fluctuations generated by the network and predict critical transitions for coupling parameters outside the observed range.

Machine learning approaches for Kuramoto coupled oscillator systems

“…We note that in this paper, we proposed a deep learning algorithm for the inference of a network structure from a chaotic pattern. This algorithm differs from other ML algorithms used in previous studies of network inference 13,15 . So it is interesting to compare our algorithm with others in diverse perspectives.…”

“…Chaotic patterns are generated not only by single-particle nonlinear dynamic equations, but also through the cooperation of multiple elements in a system. It may be interesting to understand how these elements are interwoven and coa) Electronic mail: bkahng@kentech.ac.kr operate in a system [13][14][15] . For instance, in neurophysiology, research on classifying and capturing physiological events, such as seizures, strokes, or headaches, has been conducted by identifying the correlations among electroencephalogram (EEG) signals.…”

Detecting and Evolving Microblog Community Based on Structure and Gravity Cohesion

“…Community detection is used to format the law of the community in a static network. In fact, social networks are evolving continuously over time [21], [22]. Recently, a large number of evolving community approaches have been formed.…”

Network dynamics reconstruction from data

“…where k i is the degree of node i and ξ i is finite size fluctuations due to reduction at node i , v(x) = ∫ h(y, x)dm(y) and m is the Lebesgue measure. For a precise statement and details of the general setting see [10,38].…”